A theoretical analysis of neural firing rate function based on an integral pulse frequency modulation model

Low-pass filtering techniques have been suggested as a simple approach to recover the original input modulating information from an integral pulse frequency modulation (IPFM) process mimicking neural physiological encoding mechanisms. However, due to the non-linearity of the IPFM model and the difficulty in estimating the threshold value of neurons in vivo, it is practically implausible to recover precisely the input modulation amplitude or intensity information through simple low-pass filtering. Instead, it is found through a mathematical analysis that such demodulation is of special importance for studying the firing characteristics of neural and muscle cells. In this paper, with a single sinusoidal signal as the input modulation signal to the IPFM model, an expression for the relationship between the instantaneous firing rate and the intensity of input signals is derived. The results show that the firing rate function in terms of the modulating signal and the threshold can be reconstructed with reasonable accuracy by simple low-pass filtering.